+35 Schurman Orchards has apple trees and cherry trees. The apples and cherries that are grown at Schurman Orchards are used to produce both apple cider and cherry cider. Weekly sales commitments by the owners of Schurman Orchards require at least 50 gallons of apple cider and at least 20 gallons of cherry cider. Schurman Orchards has the weekly capacity to produce at least 100 gallons of apple cider or at least 50 gallons of cherry cider or any linear combination of apple cider and cherry cider. Each gallon of apple cider cost Schurman Orchards $4; each gallon of cherry cider cost $6.
a. Set up the appropriate linear program
b. Solve the result of (a) using the simplex algorithm.
+118608 I am not sure what you want but maybe this is it.
https://www.desmos.com/calculator/swbgll5vmh
On the graph the x axis represents gallons of apple cider produced
and the y axis represents gallons of cherry cider produced.
"The apples and cherries that are grown at Schurman Orchards are used to produce both apple cider and cherry cider. Weekly sales commitments by the owners of Schurman Orchards require at least 50 gallons of apple cider and at least 20 gallons of cherry cider.
You need more than 50 gallons of apple cider and mor than 20 gallons of cherry cider so I marked the region on the grid where this is true. (It is where the red and blue overlap. Our answer must be in this overlap region.
Schurman Orchards has the weekly capacity to produce at least 100 gallons of apple cider or at least 50 gallons of cherry cider or any linear combination of apple cider and cherry cider.
I drew a line joining (0,50) and (100,0)
Which is y=-0.5x+50
Since the production has to be "at least" this, I made it y>-0.5x+50 (which does not make a lot of sense to me but not to worry) Anyway now we have a new red overlap region.
Now The dollar cost of production is c=4x+6y
So the most cheapest production would be in the overlap area as described above BUT on or above the line y=-0.5x+50
where c from the above equation is smallest. (because c IS the cost) It will always be on a corner.
I have made c a slider on the graph so you can change it and see what happens.
The smallest c is at (50,25) that is the most cost effective production will be.
You can move the slider to see what I mean,
So the cheapest production that meets all the criterion is : apple cider 50 gallons and cherry cider 25 gallons.
The cost of this production will be $350.
